EASY WAY TO SOLVE A TRIANGLE PROBLEM

Many student confuse to solve a triangle problem wheather to find an all the three angle or the three sides of the triangle.Triangle have at 6 type or shape.All the type have a characteristic and student have to remember and know all the shape and characteristic.First of all,check wheather the triangle fall in the right angle triangle.Let see the example,given a triangle ABC,where a=3,b=4 and c=5,let we check wheather it is a right angle triangle,law of phytagorean a^2 + b^2=c^2,so 25= 9+16,so this is a right angle triangle where C is 90 degree and opposite side is c or hypotenuse, angel B +A = 90 degree and opposite B is b side and opposite A  is a side.Remember this tips.

If only we know the triangle is right angle,law of sine and cosine is,sin A=a/c,Cos A=b/c and tan A=a/b so same as angle at B,sin B=b/c,Cos B=a/c and tan B=b/a.That all for case 1.

Case 2:

If the given triangle ABC,where a=4,b=6 and c=7, c^2=a^2 + b^2,49 not equal to 52,so this is not right angle triangle.If c^2 < a ^2 +b^2 or c^2> a^2 + b^2,so this is not a right angle triangle type.There 5 other type of triangle.l.Equilateral triangle-this triangle have same length for the three sides and all the angle inside value is 60 degree each one.2).Isosceles triangle-this type of triangle have 2 sides with same length and  2 angle with same value  opposite to the 2 same length sides,3).Scalene triangle is the triangle that has 3 sides of different length and different length.4).Acute triangle is the triangle which all the three angle value is less than 90 degree and obtuse triangle is the triangle which one of the angle are more than 90 degree.The longest side is opposite the largest angle.

How to solve the 5 type of triangle?

All the student must remenber Law of Sine and Law of Cosine.Law of sine, a/Sin A=b/Sin B=c/Sin C or Sin A/a=Sin B/b= Sin C/c and Law of Cosine is a^2=b^2 + c^2 - 2bcCos(A),b^2=a^2 + c^2 -2ac Cos(B) and c^2=a^2 + b^2 - 2 ab Cos(C).Tangent are SinӨ/CosӨ.All the question must given either 3 of value to solve the trangle.1).1 side + 2angle ,2).2 sides + 1 angle,3). 3 sides by applying the Sine Law and Cosine Law,all the problem solve.

Example ,given ABC triangle with a= 4,b=7,c=9,find the angle of A,B and C.First check wheather the triangle is right triangle.c^2=a^2 + b^2= 81≠16 +  49 so Law of Cosine can be apply. Let a^2=b^2 + c^2 -2bc Cos (A),by subsitute 16=49 + 81 -2(7)(9)Cos(A),Cos A=58/126,A=81.86,so using the Law of sine all the sides and angles can be solved.

Another type of triangle is sphere triangle.The Law sine and cosine is different from the above where Sin a/Sin A=Sin b/Sin B=Sin c/ Sin C and Law of cosine is cos a=cos b cos c+sin b sin c Cos A.Cos b=Cos a Cos c +Sin a Sin c Cos B and Cos c=cos a Cos b = Sin a Sin b Cos C.These type of triangle is purposely used to find a direction of place on the earth using latitude and longitude and value of a,b and c are in degree.

That all guys.Thank you